Subgroups — C₃×#1366 #67926

Order 384.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#499	C₂	1	1	yes	maximal, characteristic
2	C₃×#364	C₂	1	1	yes	maximal, characteristic
3	C₃×#364	C₂	1	1	yes	maximal, characteristic
4	#1366	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
5	C₃×#125	C₄	1	2	yes	—
6	C₃×M₃₂	—	2	1	no	—
7	C₃×M₃₂	—	2	1	no	—
8	C₃×#107	—	2	1	no	—
9	C₃×#106	—	2	1	no	—
10	C₃×C₄×C₈	C₂²	1	1	yes	characteristic
11	#499	C₂×C₃	1	1	yes	characteristic
12	#364	C₂×C₃	1	1	yes	characteristic
13	#364	C₂×C₃	1	1	yes	characteristic
14	C₂×C₃×C₈	D₄	1	1	yes	characteristic
15	C₂×C₃×C₈	D₄	1	1	yes	characteristic
16	C₃×C₄⋊C₄	—	2	2	no	—
17	C₃×C₄⋊C₄	—	4	2	no	—
18	C₃×C₄²	C₂×C₄	1	1	yes	characteristic
19	C₃×C₁₆	—	4	1	no	—
20	C₃×C₁₆	—	4	1	no	—
21	#125	C₃×C₄	1	2	yes	—
22	M₃₂	—	2	1	no	—
23	M₃₂	—	2	1	no	—
24	#107	—	2	1	no	—
25	#106	—	2	1	no	—
26	C₄×C₈	C₂²×C₃	1	1	yes	characteristic
27	C₂×C₃×C₄	—	2	1	no	—
28	C₂×C₃×C₄	—	4	2	no	—
29	C₂×C₃×C₄	C₂²⋊C₄	1	1	yes	characteristic
30	C₃×C₈	SD₁₆	1	1	yes	characteristic
31	C₃×C₈	SD₁₆	1	1	yes	characteristic
32	C₃×C₈	Q₁₆	1	1	yes	characteristic
33	C₃×C₈	Q₁₆	1	1	yes	characteristic
34	C₂×C₈	C₃×D₄	1	1	yes	characteristic
35	C₂×C₈	C₃×D₄	1	1	yes	characteristic
36	C₄⋊C₄	—	2	2	no	—
37	C₄⋊C₄	—	4	2	no	—
38	C₄²	C₂×C₃×C₄	1	1	yes	characteristic
39	C₁₆	—	4	1	no	—
40	C₁₆	—	4	1	no	—
41	C₂²×C₃	#100	1	1	yes	characteristic
42	C₃×C₄	—	4	1	no	—
43	C₃×C₄	—	8	2	no	—
44	C₃×C₄	#103	1	1	yes	characteristic
45	C₃×C₄	#103	1	1	yes	characteristic
46	C₂×C₄	—	2	1	no	—
47	C₂×C₄	—	4	2	no	—
48	C₂×C₄	C₃×C₂²⋊C₄	1	1	yes	characteristic
49	C₈	C₃×SD₁₆	1	1	yes	characteristic
50	C₈	C₃×SD₁₆	1	1	yes	characteristic
51	C₈	C₃×Q₁₆	1	1	yes	characteristic
52	C₈	C₃×Q₁₆	1	1	yes	characteristic
53	C₂×C₃	—	2	1	no	—
54	C₂×C₃	#333	1	1	yes	characteristic
55	C₂²	C₃×#100	1	1	yes	characteristic
56	C₄	—	4	1	no	—
57	C₄	—	8	2	no	—
58	C₄	C₃×#103	1	1	yes	characteristic
59	C₄	C₃×#103	1	1	yes	characteristic
60	C₃	#1366	1	1	yes	characteristic, direct product factor, Sylow
61	C₂	—	2	1	no	—
62	C₂	C₃×#333	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₃	#333
commutator	C₄²	C₂×C₃×C₄
Frattini, cosocle	C₄×C₈	C₂²×C₃
prime radical	C₂²×C₃	#100
LCS	G ▷ C₄² ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃ ◁ C₂×C₃×C₄ ◁ C₃×C₄×C₈ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
4. #1366	C₃	direct (N × H)
60. C₃	#1366	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃×#499	2
C₃×#364	2
#1366	3

Subgroups — C3×#1366 #67926

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#1366 #67926